How to Find the Factors of a Number

The factors of a number are all those numbers that can divide evenly into the number with no remainder. The greatest factor of a number is the number itself, so you can always list all the factors of any number because you have a stopping point.

Follow these steps to list all the factors of a number:

Begin the list with 1, leave some space for other numbers, and end the list with the number itself.

Test whether 2 is a factor — that is, see whether the number is divisible by 2.

If it is, add 2 to the list, along with the original number divided by 2 as the second-to-last number on the list.

Test the number 3 in the same way.

Continue testing numbers until the beginning of the list meets the end of the list.

An example should help make this clear. Suppose you want to list all the factors of the number 18. According to Step 1, begin the list with 1 and end it with 18:

1 . . . 18

Every number — whether prime or composite — is divisible by itself and 1. So automatically, 1 and 18 are both factors of 18.

Next, test whether the number 2 is a factor of 18:

18 ÷ 2 = 9

Because 2 divides 18 without a remainder, 2 is a factor of 18. So both 2 and 9 are factors of 18, and you can add them both to the list:

1 2 . . . 9 18

Notice that 9 is added as the second-to-last number of the list. Doing this reminds you that you don’t have to check any number higher than 9.

Now test 3 in the same way:

18 ÷ 3 = 6

So both 3 and 6 are factors of 18:

1 2 3 . . . 6 9 18

At this point, you’re almost done. You have to check only the numbers between 3 and 6 — that is, the numbers 4 and 5:

18 ÷ 4 = 4 r 2

18 ÷ 5 = 3 r 3

Thus, neither 4 nor 5 is a factor of 18, so this is a complete list of the factors of 18: